13. x 5
4 x 5
7
Algebra 2 CP
Name__________________
Assignment_____________
Simplify the expression using the properties of radicals and rational exponents. Final answers should be in radical form. No negative exponents, no radicals in the denominator!
1.
4
 
3
3
4. 125 4
2
3
4
7. 6 3
2.
4
 
4
2
5. 32 3
8.
4 3
1
4 3
2
3
3. 36 2
6.
1 4
7 3

7 3
9.
1 1
5 4

3 4
10.

 3 2
3


2
11.
5 4 x 3
 x 3 12.

 x 2
1



2
14. x 5
4 x 5
1
15. 3 81 x
2 y
3
16.
3 4
16 x 17.
4 32
4 2
18. 4
11
121

Perform the indicated operation. Assume all variables are positive.
19. 6 3 5 x
4 
5 x 3 5 x 20. 5 5

2 45
Write the expression in simplest form. Assume all variables are positive.
22. x
3 y
4 z
 xyz
4
23. 4 2

4 8
21. 2 x
3 
7 x
3
Solve the equation. Round the result to the nearest hundredth when appropriate.
24. 2 x
5 
73

53 25. 2
 x

3

4 
162
26. Find the radius of a sphere with a volume of 589 cubic centimeters. ( V

4
3
 r
3
)
27.
A wooden deck and a circular swimming pool cover an area of 514.16 square feet of the
lawn. The rectangular deck is 20 feet wide and 10 feet long and the pool is placed to the side of the deck.
What is the radius of the pool?
Let f ( x ) = 7 x 1/2 
2, g ( x ) =
 x 1/2 + 4, and h ( x ) =

4 x 1/3 + 1. Perform the indicated operation and state the domain.
28. f ( x ) + g ( x ) 29. f ( x ) - h ( x ) 30. h ( x ) + g ( x )

39. f
Let f ( x ) = 4 x 2 , g ( x ) = x 1/2 , and h ( x ) =
31. f x


4 x

16
. Perform the indicated operation and state the domain.
32. f g
 
  33. h x

34.
h
 f
  
Find an equation for the inverse relation.
36. y

2 x

5 37. f
35. f
 g
  

1
5 x

3 38. f
 

4 x
7

4 x 2 
1 , x

0 40. y

1
2

1
3 x 41. f
 

5 5 x

4

Verify that f and g are inverse functions.
42. f
 

7 x

4 ; g
 
 x

7
4
44. f

3
 x ; g
 

3
 x
4 3 . f
45. f
 x 5 ; g
 
 5 x
 x
2 
5 , x

0 ; g
 x

5
Determine whether the inverse of the function graphed below is a function.
46.
Solve the equation. Check your solution.
1
48. x 2

4

1 49. 3
47.
4

3 x

21 50. 3 x

4

2
3

3
51. 2
 x

1
 1
2

3

7 52. 2 3 2 x

3

7

10 53.
 x

4
 1
3

2
 
6

54. 6 3 x

3

2

1
2
56.
 x

2
 3
4
58. x

3


8
2 x

7
60. x

1

3 x

3
55. 2 x 2
3

3

19
57.

3 x

21
 4
3

9

90
59. 3 4 x

9
 3 2 x

4
61. 4 x

12

1

2 x

7
62. The velocity of a free falling object is given by V

2 gh where V is velocity (in meters per second), g is acceleration due to gravity (in meters per second squared), and h is the distance (in meters) the
object has fallen. The value of g depends on which body/planet is attracting the object. If an object hits the
surface with a velocity of 30 meters per second, from what height was it dropped in each of the following
situations? a. You are on Earth where g = 9.81 m/s 2 . b. You are on Mars where g = 3.72 m/s 2 .

ANSWERS
1. 8 2. 81 3. 216 4. 25 4 5 5. 8
3
2
6. 7 3 7
2
7. 6 8.
3 4 9. 4 15 10. 27
11. x
3
12.
1 x
13.
5 3 x 14.
5 x
2 x
15. 3 y 3 3 x 2
16. 2 x 3 2 x 17. 2 18.
4
11
3
11
19. 11 x 3 5 x 20.

5
21. 9 x x 22. x
2 y
2 z
2 yz 23. 2 24. -1.58 25. x = 0, -6
26. 5.2 cm
29. 7
27. r = 10 feet x

4 3 x

3 ; D: [0, ∞)
28. 6 x

2 ; D: [0, ∞)
30.
 x

4 3 x

5 ; D: [0, ∞)
31. 4 x
2
33. x ; D: [0, ∞) 32. 4 x x

4

16

4 x
2
; D:

 
, 16
 
16 ,


34. x ; D: (0, ∞) x
2

1

4
; D:

 
,

2
 

2 , 2
 
2 ,


35. 4x; D: [0, ∞) 36. f

1  x
2
2

5
37.
38. f

1
 

7 x
4
39. f

1  x

1
2
40.
41. f

1  x
5
5

4 f f

1

1
42 – 45. Need to guarantee f(g(x)) = x and g(f(x)) = x
46. No 47. Yes 48. x = 25


5 x

15

3 x

3
2
49. x = -15
13
50. x =
27
51. x = 26
3
52. x =
16
55. x = 4
53. x = -68
56. x = 18
54. x =
191
64
57. x = 2 and -16
58. x = 4 59. x =
5
2
60. x =4
61. x = 1 62. h = 45.87 meters 63. h = 120.97 m